Hardesty/Hardesty3

surface fitting problem (larger version)
Name Hardesty3
Group Hardesty
Matrix ID 2833
Num Rows 8,217,820
Num Cols 7,591,564
Nonzeros 40,451,632
Pattern Entries 40,451,632
Kind Computer Graphics/Vision Problem
Symmetric No
Date 2015
Author S. Hardesty
Editor T. Davis
Structural Rank 7,591,564
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 0%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
Download MATLAB Rutherford Boeing Matrix Market
Notes 
Surface fitting problem for visualization, Sean Hardesty              
                                                                      
Visualization of 3D structures in the earth                           
                                                                      
The Hardesty3 matrix is an interpolation matrix stacked above a       
weighted Laplacian, to to fit a surface z(x,y) to a set of points     
in R^3 subject to a smoothness constraint enforced via regularization.
Hardesty2 is a smaller version of this problem.                       
                                                                      
For the big matrix (Hardesty/Hardesty3), sparse QR (via SuiteSparseQR,
or SPQR) finds an R factor and a set of Householder vectors (Q.H) with
about 150 million nonzeros.  Sparse LU factorization (with UMFPACK    
v5.7.1) sees very high fillin (about 2.5 billion nonzeros in L+U).    
                                                                      
The Hardesty1 matrix is a simple discretization of a 2D biharmonic    
operator with some Lagrange multiplier constraints used for smoothing.